{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from sklearn.linear_model import LinearRegression\n",
    "import statsmodels.api as sm\n",
    "import statsmodels.formula.api as smf"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "y = np.arange(1, 25, 0.25)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "# linear relationship with contant variance of residual\n",
    "# x1 和 y具有恒定的线性关系, 具有稳定的残差方差\n",
    "x1 = y.copy() + np.random.randn(96) # 生成96个正太分布的随机数"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "# non contant variance with residuals \n",
    "# x2和y2具有不稳定的残差方差\n",
    "x2 = y.copy()\n",
    "y2 = x2 + np.concatenate((np.random.randn(20)*0.5,\n",
    "                                np.random.randn(20)*1, \n",
    "                                np.random.randn(20)*4, \n",
    "                               np.random.randn(20)*6, \n",
    "                               np.random.randn(16)*8), axis=0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x396 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, (ax1,ax2) = plt.subplots(1,2 , figsize = (12,5.5) )\n",
    "\n",
    "ax1.plot(x1, y, 'o')\n",
    "ax1.set_xlabel('X1')\n",
    "ax1.set_ylabel('Y')\n",
    "ax1.set_title('Contant variance of residuals')\n",
    "\n",
    "ax2.plot(x2, y2, 'o')\n",
    "ax2.set_xlabel('X2')\n",
    "ax2.set_ylabel('Y')\n",
    "ax2.set_title('Non contant variance of residuals')\n",
    "\n",
    "fig.tight_layout()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "lr = LinearRegression()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "LinearRegression(copy_X=True, fit_intercept=True, n_jobs=1, normalize=False)"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lr.fit(x1.reshape(-1,1),y.reshape(-1,1))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "LinearRegression(copy_X=True, fit_intercept=True, n_jobs=1, normalize=False)"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lr2 = LinearRegression()\n",
    "lr2.fit(x2.reshape(-1,1),y.reshape(-1,1))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x396 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "\n",
    "fig, (ax1,ax2) = plt.subplots(1,2 , figsize = (12,5.5) )\n",
    "\n",
    "ax1.plot(x1, y, 'o')\n",
    "ax1.set_xlabel('X1')\n",
    "ax1.set_ylabel('Y')\n",
    "ax1.set_title('Contant variance of residuals')\n",
    "ax1.plot(x1, lr.predict(x1.reshape(-1,1)))\n",
    "\n",
    "ax2.plot(x2, y2, 'o')\n",
    "ax2.set_xlabel('X2')\n",
    "ax2.set_ylabel('Y')\n",
    "ax2.set_title('Non contant variance of residuals')\n",
    "ax2.plot(x2, lr2.predict(x2.reshape(-1,1)))\n",
    "\n",
    "fig.tight_layout()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Quantile regression**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "data = pd.DataFrame(data={'X': x2, 'Y':y2})"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "      q         a         b        lb        ub\n",
      "0  0.05  0.794692  0.531205  0.371151  0.691260\n",
      "1  0.95 -0.731052  1.713815  1.427542  2.000089\n",
      "{'lb': 0.8860452058945112, 'b': 1.0299725445856005, 'ub': 1.1738998832766898, 'a': 0.05478414224981387}\n"
     ]
    }
   ],
   "source": [
    "mod = smf.quantreg('Y ~ X', data)\n",
    "res = mod.fit(q=.5)\n",
    "\n",
    "quantiles  = np.array((0.05, 0.95))\n",
    "def fit_model(q):\n",
    "    res = mod.fit(q=q)\n",
    "    return [q, res.params['Intercept'], res.params['X']] + \\\n",
    "            res.conf_int().loc['X'].tolist()\n",
    "    \n",
    "models = [fit_model(x) for x in quantiles]\n",
    "models = pd.DataFrame(models, columns=['q', 'a', 'b','lb','ub'])\n",
    "\n",
    "ols = smf.ols('Y ~ X', data).fit()\n",
    "ols_ci = ols.conf_int().loc['X'].tolist()\n",
    "ols = dict(a = ols.params['Intercept'],\n",
    "           b = ols.params['X'],\n",
    "           lb = ols_ci[0],\n",
    "           ub = ols_ci[1])\n",
    "\n",
    "print(models)\n",
    "print(ols)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x432 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "xn = np.arange(data.X.min(), data.X.max(), 2)\n",
    "get_y = lambda a, b: a + b * xn\n",
    "\n",
    "fig, ax = plt.subplots(figsize=(8, 6))\n",
    "\n",
    "for i in range(models.shape[0]):\n",
    "    yn = get_y(models.a[i], models.b[i])\n",
    "    ax.plot(xn, yn, linestyle='dotted', color='grey')\n",
    "\n",
    "yn = get_y(ols['a'], ols['b'])\n",
    "\n",
    "ax.plot(xn, yn, color='red', label='OLS')\n",
    "\n",
    "ax.scatter(data.X, data.Y, alpha=.2)\n",
    "legend = ax.legend()\n",
    "ax.set_xlabel('X', fontsize=16)\n",
    "ax.set_ylabel('Y', fontsize=16)\n",
    "ax.set_title('Quantile regression with 0.05 and 0.95 quantiles')\n",
    "\n",
    "fig.tight_layout()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.5.5"
  },
  "toc": {
   "base_numbering": 1,
   "nav_menu": {},
   "number_sections": true,
   "sideBar": true,
   "skip_h1_title": false,
   "title_cell": "Table of Contents",
   "title_sidebar": "Contents",
   "toc_cell": false,
   "toc_position": {},
   "toc_section_display": true,
   "toc_window_display": false
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}
